The purpose of this study is to compare the effects of the experimental drug Trametinib to one of two commonly used chemotherapy treatments in subjects with advanced biliary cancer that has come back after initial treatment. The two commonly used chemotherapy treatments used in this study are 5-fluorouacil (5-FU) with leucovorin and capecitabine alone. In this study, subjects will get either the Trametinib or one of the common treatments, not both.